Frampt must not like Seath , or anyone related to him, very much. All crystal weapons sell for 1 soul, including the MLGS I believe. So assuming that Pricilla is his daughter, he doesn't really care for her things either. Is the dagger the same?

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My guess is crystal items are hard to process/digest for him. Crystal is super brittle so it likely just falls apart with little returns. The Lifehunt's lore suggests it might be some kind of semi-sentient weapon that likes to keep souls for itself. I've always envisioned it kinda like Stormbringer

So to answer your question for the Lifehunt, my guess is that it has already used whatever souls are inherent in a weapon providing small returns. Or the process of Frampt breaking it causes him harm, also leading to lost returns.